Question: ${\left[ \begin{array}{cc} -2 & 4 & 3\\ 2 & -2 & -2 \end{array} \right]-\left[ \begin{array}{cc} -2 & 3 & 4 \\ 4 & -1 &-1 \end{array} \right]= }$
Answer: The Strategy To add or subtract matrices that have the same dimensions, we add or subtract the corresponding terms from each matrix that have the same coordinates. Subtracting the Corresponding Terms ${\begin{aligned}\left[ \begin{array}{cc} {-2} & {4} & {3} \\ {2} & {-2} & {-2} \end{array} \right]-\left[ \begin{array}{cc} {-2} & {3} & {4} \\ {4} & {-1} & {-1} \end{array} \right]&= \left[ \begin{array}{cc} ({-2+2})\!\!\! &\!\!\! ({4-3})\!\!\! &\!\!\! ({3-4}) \\ ({2-4}) \!\!\!& \!\!\!({-2+1}) \!\!\!& \!\!\!({-2+1}) \end{array} \right] \\\\&=\left[ \begin{array}{cc} {0} & {1} & {-1} \\ {-2} & {-1} & {-1} \end{array} \right]\end{aligned}}$ Summary ${\left[ \begin{array}{cc} -2 & 4 & 3\\ 2 & -2 & -2 \end{array} \right]-\left[ \begin{array}{cc} -2 & 3 & 4 \\ 4 & -1 &-1 \end{array} \right]= \left[ \begin{array}{cc} 0 & 1 & -1\\ -2 & -1 & -1 \end{array} \right]}$